|k-Boson Quantum Walks Do Not Distinguish Arbitrary Graphs - Jamie Smith|
In this paper, we define k-equivalence, a relation on graphs that relies on their associated cellular algebras. We show that a k-Boson quantum walk cannot distinguish pairs of graphs that are k- equivalent. The existence of pairs of k-equivalent graphs has been shown by Ponomarenko et al. [2, 6]. This gives a negative answer to a question posed by Gamble et al. .
|Cellular Algebras and Graph Invariants Based on Quantum Walks - Jamie Smith|
We consider two graph invariants inspired by quantum walks- one in continuous time and one in discrete time. We will associate a matrix algebra called a cellular algebra with every graph. We show that, if the cellular algebras of two graphs have a similar structure, then they are not distinguished by either of the proposed invariants.
|Transmogrify - Jamie Smith|
I was born a white female in the mid twentieth century industrial America. I came into this world armed to the teeth with an arsenal of weapons. The weapons of privilege; racial privilege, economic privilege. To be a pacificst, I have to give up the weapons of privilege and go into the world completely disarmed. Peace Corps,Student.
Keywords: Language Arts & Writing; Poetry; Art; Africa
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|Algorithms for Quantum Computers - Jamie Smith|
This paper surveys the field of quantum computer algorithms. It gives a taste of both the breadth and the depth of the known algorithms for quantum computers, focusing on some of the more recent results. It begins with a brief review of quantum Fourier transform based algorithms, followed by quantum searching and some of its early generalizations. It continues with a more in-depth description of two more recent developments: algorithms developed in the quantum walk paradigm, followed by tensor n...
|Number-Theoretic Nature of Communication in Quantum Spin Systems - Chris Godsil|
The last decade has witnessed substantial interest in protocols for transferring information on networks of quantum mechanical objects. A variety of control methods and network topologies have been proposed, on the basis that transfer with perfect fidelity --- i.e. deterministic and without information loss --- is impossible through unmodulated spin chains with more than a few particles. Solving the original problem formulated by Bose [Phys...